Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x - 4$ and $ JT = 9x - 20$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x - 4} = {9x - 20}$ Solve for $x$ $ -2x = -16$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({8}) - 4$ $ JT = 9({8}) - 20$ $ CJ = 56 - 4$ $ JT = 72 - 20$ $ CJ = 52$ $ JT = 52$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {52} + {52}$ $ CT = 104$